基于四阶完全非线性Boussinesq水波方程二维波浪传播数值模型  

A 2D numerical wave model based on fourth order fully nonlinear Boussinesq equations

作　　者：房克照[1] 邹志利[1] 

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024

出　　处：《海洋工程》2011年第1期32-40,共9页The Ocean Engineering

基　　金：中央高校基本科研业务费专项资金资助项目;大连理工大学海岸和近海工程国家重点实验室;河海大学海岸灾害及防护教育部重点实验室开放基金资助项目;国家自然科学基金资助项目(51009018)

摘　　要：建立基于四阶完全非线性Boussinesq水波方程的二维波浪传播数值模型。采用Kennedy等提出的涡粘方法模拟波浪破碎。在矩形网格上对控制方程进行离散,采用高精度的数值格式对离散方程进行数值求解。对规则波在具有三维特征地形上的传播过程进行了数值模拟,通过数值模拟结果与实验结果的对比,对所建立的波浪传播模型进行了验证。同时,为了考察非线性对波浪传播的影响,给出和上述模型具有同阶色散性、变浅作用性能但仅具有二阶完全非线性特征的波浪模型的数值结果。通过对比两个模型的数值结果以及实验数据,讨论非线性在波浪传播过程中的作用。研究结果表明,所建立的Boussinesq水波方程在深水范围内不但具有较精确的色散性和变浅作用性能,而且具有四阶完全非线性特征,适合模拟波浪在近岸水域的非线性运动。The present study develops a 2D wave breaking model based on the fourth-order full nonlinear Boussinesq equations.This set of equations possesses higher accuracy in dispersion,shoaling and full nonlinearity characteristics,which enable it applicable in describing water waves in nearshore zone.The discretizationis conducted on a rectangle grid system,higher order finite difference formulas are used to approximate the spatial derivatives and high accuracy scheme is used to integrate equations in time.Kennedy et al′s eddy viscosity breaking mechanism is incorporated to mimic wave breaking.The mathematical model is run to simulate waves transformation over typical three dimensional bathymetries.The numerical results are verified against available experimental data.The satisfactory agreement between numerical results and experimental data demonstrate the validation and efficiency of the present wave breaking model.The effect of full nonlinearity on wave propagation is discussed by comparing the numerical results with those from Boussinesq model with only the second-order full nonlinearity characteristics.

关 键 词：Boussinesq水波方程 波浪传播模型 波浪破碎 涡粘 

分 类 号：TV148[水利工程—水力学及河流动力学]